Express your answer as a mixed number simplified to lowest terms. $10\dfrac{2}{20}-2\dfrac{5}{15} = {?}$
Explanation: Simplify each fraction. $= {10\dfrac{1}{10}} - {2\dfrac{1}{3}}$ Find a common denominator for the fractions: $= {10\dfrac{3}{30}}-{2\dfrac{10}{30}}$ Convert ${10\dfrac{3}{30}}$ to ${9 + \dfrac{30}{30} + \dfrac{3}{30}}$ So the problem becomes: ${9\dfrac{33}{30}}-{2\dfrac{10}{30}}$ Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{33}{30}} - {2} - {\dfrac{10}{30}}$ Bring the whole numbers together and the fractions together: $= {9} - {2} + {\dfrac{33}{30}} - {\dfrac{10}{30}}$ Subtract the whole numbers: $=7 + {\dfrac{33}{30}} - {\dfrac{10}{30}}$ Subtract the fractions: $= 7+\dfrac{23}{30}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{23}{30}$